We present a general method to study the dissymmetry of anatomical structures such as the human brain. Our method relies on the estimate of 3D dissymmetry fields, the use of 3D vector field operators, and $T^2$ statistics to compute significance maps. We also present a fully automated implementation of this method which relies mainly on the intensive use of a 3D non-rigid inter-patient matching tool. Such a tool is applied successively between the images and their symmetric versions with respect to an arbitrary plane, both to realign the images with respect to the mid-plane of the subject and to compute a dense 3D dissymmetry map. Inter-patient matching is also used to fuse the data of a population of subjects. We then describe three main application fields: the study of the normal dissymmetry within a given population, the comparison of the dissymmetry between two populations, and the detection of the significant abnormal dissymmetries of a patient with respect to a reference population. Finally, we present preliminary results illustrating these three applications for the case of the human brain.